Find the area of following quadrilateral ​

Find The Area Of Following Quadrilateral

Answers

Answer 1

Answer:

[tex]222cm^{2}[/tex]

Step-by-step explanation:

First we will find the length of BD.

By Pythagoras' Theorem,

[tex]c^{2} =a^{2} +b^{2} \\BD^{2} = AD^{2} +AB^{2} \\BD^{2} =12^{2} +16^{2} \\BD^{2} = 144+256\\BD^{2} =400\\BD = \sqrt{400} \\=20cm[/tex]

Now we will find Angle ADB.

[tex]\frac{AB}{sin(Angle ADB)} =\frac{BD}{Sin(AngleBAD)} \\\frac{16}{sin(AngleADB)} =\frac{20}{sin(90)} \\20sin(AngleADB)=16sin(90)\\20sin(AngleADB)=16\\sin(AngleADB)=\frac{16}{20} \\sin(AngleADB)=0.8\\AngleADB=sin^-1(0.8)\\=53.130deg\\[/tex]

Now we will find Area of triangle BCD

[tex]Angle BDC = 90 - Angle ADB = 90 - 53.130 = 36.87deg\\\\\\Area of Triangle BCD \\= \frac{1}{2} (BD)(CD)sin(AngleBDC)\\=\frac{1}{2} (20)(21)sin(36.87)\\= 126cm^{2}[/tex]

Then we will find the area of triangle BAD

[tex]=\frac{1}{2} (16)(12)\\= 96cm^{2} \\[/tex]

Area of quadrilateral = Area of Triangle BCD + Area of Triangle BAD

= 126+96

= [tex]222cm^{2}[/tex]

Answer 2

Answer:

A = 222 cm²

Step-by-step explanation:

it is a trapezoid

so

A = ½ (a + b) h

A = ½ (16 + 21) × 12

A = ½ 37 × 12

A = ½ 444

A = 222 cm²


Related Questions

The table shows the prices of different sizes of containers of vegetable oil.

A 3-column table with 3 rows. Column 1 is labeled Container size with entries 16 ounces, 24 ounces, 48 ounces. Column 2 is labeled Price with entries 4 dollars and 64 cents, 6 dollars and 24 cents, 16 dollars and 32 cents. Column 3 is labeled price per ounce with entries 29 cents, 26 cents, 34 cents.

Tony needs to purchase 3,600 oz of vegetable oil for his catering business. For the containers shown in the table, how much would he save by purchasing those with the lowest unit price than those with the highest unit price?

Total amount at lowest price:
Total amount at highest price:
Amount saved:

Answers

The total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The table is in the picture, please refer to the picture.

Tony needs to purchase 3,600 oz of vegetable oil for his catering business.

Lowest unit price = 26 cents per ounce

Total price at this rate = 3600×26 = 93600 cents = $936

The highest unit price = 34 cents per ounce

Total price at this rate = 3600×34 = 122400 cents = $1224

Total saving he purchases the container that has the lowest unit price:

= 1224 - 936

= $288

Thus, the total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

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Question 7 of 10
Which choices are equivalent to the expression below? Check all that apply.
3√6
A. √54
B. 18
C. √27.4
☐D. √27.√2
□E √9.6
F. 54
PREVIOUS

Answers

Step-by-step explanation:

[tex] = 3 \sqrt{6} [/tex]

[tex] = \sqrt{ {3}^{2}.6 } [/tex]

[tex] = \sqrt{9.6} [/tex]

[tex] = \sqrt{54} [/tex]

The answer is A.

Suppose f(x)=x^2 and g(x)=5x^2. Which steamy best compares the graph of g(x) with the graph of f(x)?

Answers

By understanding and applying the concepts of dilation and quadratic functions, the function g(x) is a vertically dilated version of f(x) by a factor of 5.

How to compare the graphs of two functions

In this questions we know two quadratic equations of the form y = a · x². f(x) is known as the canonical function as a = 1 and g(x) is the consequence of dilating f(x) vertically by a factor of 5. Now we proceed to present graphically between the two functions.

In a nutshell, the function g(x) is a vertically dilated version of f(x) by a factor of 5.

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Which set of ordered pairs represent a line that is perpendicular to the given set: (1,8)
(2,10)?

Answers

Using linear function concepts, it is found that a set of ordered pairs with a slope of [tex]-\frac{1}{2}[/tex] is perpendicular to the given set.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

When two sets are perpendicular, the multiplication of their slopes is -1. The set (1,8) and (2,10) has slope given by:

m = (10 - 8)/(2-1) = 2.

Then, for the perpendicular set:

2m = -1

m = -1/2.

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Select from the drop-down menu to create a statistical question Susan could ask her friends in a survey.
How many
pushups can you do
days does melanie exercise
bones are in the human body
pounds are in a kilogram

Answers

The statistical question that Susan could ask her friends in a survey is that How are push-ups important for the body?

What are statical questions?

It should be noted that statistical or research questions are the questions that an individual seeks answers to.

In this case, the statistical question that Susan could ask her friends in a survey is that How are push-ups important for the body?

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Answer: 2. How many pushups can you do

I got 100% on my online homework and here is proof.

Please mark me brainliest  : D

help i will mark as branliest​

Answers

Answer:

(a) DE = 7.5 cm

(b) Area of ΔABE = 9.33 cm2

Step-by-step explanation:

(a)   [tex]\frac{AE}{DE} =\frac{BE}{CE}[/tex]

     [tex]\frac{5}{DE} =\frac{4}{6}[/tex]

    [tex]DE=\frac{(5)(6)}{4} =\frac{30}{4} =7.5[/tex]

(b) measurements of similar triangles have a ratio of 2/3

The ratio between areas is

[tex](\frac{2}{3} )^{2} =\frac{4}{9}[/tex]

If the area of ΔCDE = 21

Then the área of ΔABE is:

[tex]21(\frac{4}{9})=\frac{(21)(4)}{9} =\frac{84}{9} =9.33[/tex]

Hope this helps

write 9 430 049 in international number system

Answers

Step-by-step explanation:

9, 430, 049 = 9 million four hundred thirty thousand and fourtynine....

[tex]...[/tex] :)..

The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the tC system of equations for lines A and B?
O (3, 4) is the solution to both lines A and B.
© (3, 4) is the solution to line A but not to line B.
O (0, 2) is the solution to both lines A and B.
O (0, 2) is the solution to line A but not to line B.

Answers

Answer:

the answer is (3,4) is the solution to line A but to not line B

can someone please help mee(20 points and i will give brainliest!!!)

Answers

Answer:

(5,2)

Maximum

5

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\texttt{\:Coordinates of vertex = (5,2)}[/tex]

[tex]\texttt{The graph has a maximum} [/tex]

[tex]\tt \: Axis\:\: of \:\; symmetry : x = 5\ [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

Coordinate of vertex is the point where there's a unique (only one) value of y for x :

[tex]\qquad \tt \rightarrow \: (5,2)[/tex]

Since it's a downward parabola, it doesn't have defined minima, as it's value reach [ - infinity ]

and hence, it has a maximum, at the vertex.

Axis of symmetry is the line that divides the parabola into two equal regions that are mirror images of each other.

it is the line passing through vertex and parallel to y - axis.

[tex]\qquad \tt \rightarrow \: x = 5[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

(9x + 1) − (−7x² + 4x + 10)

Answers

Answer:

7x² + 5x - 9

Step-by-step explanation:

(9x + 1) - (- 7x² + 4x + 10) ← distribute parenthesis by - 1

= 9x + 1 + 7x² - 4x - 10 ← collect like terms

= 7x² + 5x - 9

which statement is true about the function?​

Answers

The correct answer is option D which is the function is even because of its symmetry about the y-axis.

What is even function?

The function which remains unchanged when the negative value of the variable is filled in the function is called an even function and this function is symmetric about the y-axis.

Given function:-

f(x) = 3x⁴+2x²

Now put the value x = -x in the function

f(-x) = 3( -x⁴)+2(-x²)

f(-x) = 3x⁴ + 2x²

f(-x) = f(x)

here we can see that when we put the value of negative x the function remains unchanged.

Therefore the correct answer is option D which is the function is even because of its symmetry about the y-axis.

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According to the Rational Root Theorem, what are all the potential rational roots of f(x) = 15x11 – 6x8 + x3 – 4x + 3?

Answers

All potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational rots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

The rational root theorem suggests that for a polynomial function

f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

In the question, we are asked to find the potential rational roots of

f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3.

Comparing the given polynomial function with the standard polynomial function f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₂x² + a₁x¹ + a₀, we can say aₙ = 15, and a₀ = 3.

By rational root theorem, we know that all potential rational roots can be given by the formula p/q, where p is the set of all factors of ±a₀ and q is the set of all factors of ±aₙ.

Therefore, we can say that p = {factors of ±3} and q = {factors of ±15},

or, p = {±1, ±3}, q = {±1, ±3, ±5, ±15}.

Now, we can write all potential roots by calculating p/q.

p/q = {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}

Therefore, all potential rational roots of f(x) = 15x¹¹ - 6x⁸ + x³ - 4x + 3, going by the rational roots theorem are {±1, ±1/3, ±1/5, ±1/15, ±3, ±3/5}.

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What is the value of x/2 + 4 when x = 6?

Answers

Step-by-step explanation:

solution:

here,

x/2+4

= 6/2+4 ( x = 6 )

= 3+4

= 7

Answer:

7

Step-by-step explanation:

x/2 + 4

=> 6/2 + 4 (x=6)

=> 3 + 4

=> 7

Solve the equation 4 sin x - cosec x =cot x for 0° < x < 360°. ​

Answers

For this question, I will be writing 'csc' instead of 'cosec'

[tex]4\sin x-\csc x=\cot x\\\\4\sin x-\frac{1}{\sin x}=\frac{\cos x}{\sin x}\\\\4\sin^{2} x-1=\cos x\\\\4(1-\cos^{2} x)-1=\cos x\\\\4-4\cos^{2} x-1-\cos x=0\\\\4\cos^{2} x+\cos x-3=0\\\\ (4\cos x-3)(\cos x+1)=0\\\\\cos x=\frac{3}{4}, 1\\\\\therefore \boxed{\cos^{-1} \left(\frac{3}{4} \right), 180^{\circ}, 360^{\circ}-\cos^{-1} \left(\frac{3}{4} \right)}[/tex]

A small company manufactures picnic tables. The daily fixed cost is 1,200 and the variable cost is $45 per table. How many picnic tables can be produced for a total daily cost of 4,800.

Answers

Using a linear function, it is found that 80 picnic tables can be produced for a total daily cost of 4,800.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the daily fixed cost of 1200 as the y-intercept, and the variable cost of 45 as the slope, the linear function for the cost of producing n picnic tables is given by:

C(n) = 1200 + 45n.

Now, we have to solve for n when C(n) = 4800, hence:

1200 + 45n = 4800

45n = 3600

n = 3600/45

n = 80.

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A business rents cars for $100 a day and vans for $200 a day. One day, it rented a total of 22 vehicles
and made a total of $2900. What is a possible number of cars and vans it rented that day?

Answers

Answer:

Vans - 7

Cars - 15

Step-by-step explanation:

$200 * 7 = $1400

$100 * 15 = $1500

$1400 + $1500 = $2900

g(x) =2x+3, find g(-3)

Answers

The value of g(-3)=-9

The function is a relation between two sets X and Y which are one-one or many-one. Here set X is called the domain and set Y is called codomain.

For example: f(x)=3x+9

To get the value of the function at any point of x, we have to put the number in the function to get its function value.

For example the value of f(x) in above function at x=a will be f(a)=3a+9

Similarly given function in the question

g(x)=2x+3

to get the value of g(x) at x=-3 put the value of x in the function,

g(-3)= 2(-3)+3 = -3

Therefore the value of g(-3) is -3.

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PLEASE HELP
If 2 pounds is equal to 3 dollars, which of the following is incorrect?
A. 11 pounds is 16.50 dollars
B. 28 pounds is 44 dollars
C. 10 pounds is 15 dollars
D. 23 pounds is 34.50 dollars

Answers

Therefore, the incorrect statement is option B, which states that 28 pounds is equal to 44 dollars. The correct value should be 42 dollars.

To determine which statement is incorrect, we can use the given conversion rate of 2 pounds being equal to 3 dollars and evaluate each option accordingly:

A. 11 pounds is 16.50 dollars:

To check this, we can multiply 11 pounds by the conversion rate:

11 pounds * (3 dollars / 2 pounds) = 16.50 dollars

This statement is correct.

B. 28 pounds is 44 dollars:

Using the same calculation:

28 pounds * (3 dollars / 2 pounds) = 42 dollars

This statement is incorrect because 28 pounds would actually be equal to 42 dollars, not 44 dollars.

C. 10 pounds is 15 dollars:

Again, applying the conversion rate:

10 pounds * (3 dollars / 2 pounds) = 15 dollars

This statement is correct.

D. 23 pounds is 34.50 dollars:

Using the conversion rate:

23 pounds * (3 dollars / 2 pounds) = 34.50 dollars

This statement is correct.

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Please help me with this question 1/11

Answers

The value of a₄₃ is 3.

What is Matrices?

Matrices is a plural form of a matrix, which is a rectangular array or a table where numbers or elements are arranged in rows and columns.

Here,  aₓₙ is the element of matrix in which x represents the number of row and n represents the number of column of element.

So, a₄₃ means element from 4th row and 3rd column.

4th row  =  [2  9   3   7]

3rd column = [tex]\left[\begin{array}{ccc}8\\6\\1\\3\end{array}\right][/tex]

the common value between them is 3.

Thus, the value of a₄₃ is 3.

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when you purchase a new car, what kind of tax will you usually pay

Answers

Answer:

Whether you're buying a new car or a used car, or even leasing a car, you'll have to pay state sales tax. Nearly every state has a sales tax, ranging from under 3 percent to over 8 percent. The national average in the United States is 5.75 percent.

Please mark brainlest!

Find the least common denominator for these
two rational expressions.
8
-9
3a²
-
a

Answers

The common denominator is 3a²

Which of the following is the appropriate notation when calculating
conditional probabilities?
A. P(EF)= P(E)+ P(F)- P(EUF)
B. P(EIF)=P(EnF)
P(F)
OC. P(EIF)=P(EA)
P(E)
D. P(EUF)=P(E) + P(F)-P(EF)
SUBMIT

Answers

The following are the appropriate notations is P(EIF)=P(E n F) / P(F).

What is Conditional Probability?

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

As, from the property of conditional probability

P(EIF)=P(E n F) / P(F)

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What is the formula for capacity of a prism?

Answers

Answer:

The prism volume formula is B*h B (area of one end) =0.5*1000*566 = 283,000 mm 2 (area of a triangle) H (length/height of prism) = 1000 mm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Any prism volume is equal to the area of the base (B) multiplied by the height of prism (H)  

V = BH

Now, to find the area of the base you need this formula : B = 1/2 h(b1+b2), then multiply by the height of the prism.

The nature of a graph, which has an even degree and a positive leading coefficient will be

Answers

The nature of a graph, which has an even degree and a positive leading coefficient will be up left, up right position

What is the nature of the graph of a quadratic equation?

The nature of the graphical representation of a quadratic equation with an even degree and a positive leading coefficient will give a parabola curve.

Given that we have a function f(x) = an even degree and a positive leading coefficient. i.e.

y = f(x) = 2x²+ 4

The domain of this function varies from -∞ < x < ∞ and the parabolic curve will be positioned on the upward left and upward right x-axis.

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Solve for k in g=k-a.​

Answers

Answer:

k = g + a

Step-by-step explanation:

g = k - a ( add a to both sides )

g + a = k , that is

k = g + a

The gravel path is 5.6 cm long

Answers

What about the grass

Which polynomial is equal to the sum of polynomials 1 and 2?
Polynomials 1 and 2 are represented below with tiles.
Polynomial 1
X²X²

Polynomial 2
A. 2x²+2x+1
OB. 5x² + 4x+6
OC. 7x² +6x+7
OD. 7x² +6x+5

Answers

The polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

What is a polynomial?

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved. Example, x² + 3x + 5.

As per the given informations, the first polynomial is 2x² + 2x + 1.

The second polynomial equal is 5x² + 4x + 6.

Now, the sum of the two polynomial can be written as,

Sum = 5x² + 4x + 6 + 2x² + 2x + 1 = 7x² + 6x + 7

Therefore, the polynomial 7x² + 6x + 7 is equal to the sum of polynomials 1 and 2.

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if 13n-6 = 98 what is the value of n​

Answers

Answer:

n = 8

Step-by-step explanation:

13n-6 = 98

Solution:

13n = 98+613n = 104n = 104/13n = 8

Hence the value of n is 8.

13n - 6 = 98

13n = 98 + 6

13n = 104

n = 104/13

n = 8

Solve for the value of x:-
7(x+2)=35​

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:x = 3 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 7(x + 2) = 35[/tex]

[tex]\qquad \tt \rightarrow \: 7x + 14 = 35[/tex]

[tex]\qquad \tt \rightarrow \: 7x = 35 - 14[/tex]

[tex]\qquad \tt \rightarrow \: 7x = 21[/tex]

[tex]\qquad \tt \rightarrow \: x = \cfrac{21}{7} [/tex]

[tex]\qquad \tt \rightarrow \: x = 3[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

If you vertically stretch the cubic parent function, f(x) = x3, what is the
equation of the new function?

Answers

in order to vertically stretch the parent function, you have to make the absolute value of the coefficient of x^3 larger. meaning that the coefficient of x^3 has to be greater than one or less than negative one
Other Questions
Help anyone? Simple problem Read the excerpt from Act I, scene ii of Romeo and Juliet.Benvolio: Tut! you saw her fair, none else being by,Herself poisd with herself in either eye;But in that crystal scales let there be weighdYour ladys love against some other maid 85That I will show you shining at this feast,And she shall scant show well that now shows best.Romeo: Ill go along, no such sight to be shown,But to rejoice in splendour of mine own.Romeo decides to attend the Capulets party because he wants to What does the conflict in this story show about the character of Monica? From the age of 14 onward, Monica never stopped working. She studied hard to make straight As, became a member of five different school clubs, and even worked at a fast-food restaurant after school. By the time she was an adult, Monica finally succeeded. She took a job that paid more than she could ever spend, although she worked 14 hours a day, even on weekends. One day, she collapsed from exhaustion. The doctor said the stress was killing her and she needed to take some time off. The doctor asked what she did in her spare time. She only blinked in response, unable to answer. What does the conflict in this story show about the character of Monica ? From the age of 14 onward , Monica never stopped working . She studied hard to make straight As , became a member of five different school clubs , and even worked at a fast - food restaurant after school . By the time she was an adult , Monica finally succeeded . She took a job that paid more than she could ever spend , although she worked 14 hours a day , even on weekends . One day , she collapsed from exhaustion . The doctor said the stress was killing her and she needed to take some time off . The doctor asked what she did in her spare time . She only blinked in response , unable to answer . How does this scene affect the play?It leaves the question unanswered as to whether Tomreally goes to the movies or goes drinking.It demonstrates how Tom continues to emotionallydetach himself from the situation at the apartment.It leads to the conclusion of the play and Tom's closingspeech where he admits that he is finally leaving.It shows that Tom finally stops caring about what willhappen to Laura in the future. What is the ground distance between A and B . Measure 16cm from the paper if the scale is 1:50,000 What is the equation of the line perpendicular to 2x - 3y = 13 that passes through the point (-6, 5)?y=x+9y=-3x-4y=-x-13y-x-1 Mary is going to roll a six-sided die. What is the probability that the die lands on the number 3? Input your answer in fraction form Brandon is a running back for his local high school football team. In the last game, he carried the ball 8 times. In the first 5 carries, he gained 6 yards, 12 yards, and 4 yards before losing 2 yards and then losing additional yards. His last 7 carries combined for yards. What was his total net yardage for the game? Kent bought a $1,000, 20-year U.S. Treasury bond that paid six percent annual yield when he was 22. How much would that bond be worth 20 years later when it matured? a drone traveling horizontally at 120m s over a flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground the trajectory of the package is given by x 120t y 4.9t 2 4500 define peace culture How can technological change create political instability? Which of Cyril's actions does Saki exaggerate in "The Storyteller" to create satire? Select three options.disobeying his auntasking questions about everythingtalking back to his auntencouraging the bachelor to tell a storycommenting on the two stories he is told who was the first president of Lebanon? A study by carnegie mellon university showed that drivers talking on cell phones can miss seeing ......% of their driving environment, including pedestrians and green lights (strayer, d. l. 2007). 20 10 50 At minimum, what initial actions should be performed within 10 minutes of mrs. archers arrival at the emergency department? Active citizenship is a core feature of the democratic process.Please select the best answer from the choices providedTF Simplify the expression by combining liketerms: Algebra 1 What is the oxidation state of Hg in Hg2Cl?O A. +1OB. -1O C. +2OD. -2 All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? m e = startfraction z times s over startroot n endroot endfraction.